Russel, not sure I understand?
ReSpot is not designed to remote-control the spotify client on your PC, but rather the server component “Servify”. So in essence – you don’t need the spotify client running on your PC when using ReSpot.
There are plans to design a Desktop application that will remote control Servify too (then you can use that on your PC when the phone isn’t around or it’s more convenient with a desktop application).

If you press a track in the search tab or playlist tab, then it will be queued up in the Playback tab- from there you can start music playback (by clicking a song in the queue or the play button)

Oh, that doesnt sound right… Should be able to queue more than one track. And def. play the songs!
What O/S do you have on your computer? Are you using Servify/C# or Servify/J? Is there anything written in the logs?
Don’t hesitate to send me an e-mail and we can debug the issue!